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| 184_notes:conservation_theorems [2018/05/15 17:43] – curdemma | 184_notes:conservation_theorems [2021/07/06 17:36] – bartonmo |
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| Chapters 18 and 19 (and Chapters 2, 3, 6, 11, and 13) in Matter and Interactions (4th edition) | Chapters 18 and 19 (and Chapters 2, 3, 6, 11, and 13) in Matter and Interactions (4th edition) |
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| [[184_notes:symmetry|Next Page: Symmetry and Mathematical Tools]] | /*[[184_notes:symmetry|Next Page: Symmetry and Mathematical Tools]] |
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| [[184_notes:magnetic_field|Previous Page: The Magnetic Field]] | [[184_notes:magnetic_field|Previous Page: The Magnetic Field]]*/ |
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| ===== Conservation Theorems ===== | ===== Conservation Theorems ===== |
| {{youtube>N5s0mi7BV6g?large}} | {{youtube>N5s0mi7BV6g?large}} |
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| ==== Linear and Angular Momentum Conservation in E&M ==== | ===== Linear and Angular Momentum Conservation in E&M ===== |
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| We have not talked much about linear and angular momentum conservation in an electromagnetic system because they extend beyond the scope of this course. This is because to truly understand the relationship between these and the electromagnetic field, we must develop an understanding that the electromagnetic field can have linear and angular momentum. That's right, the field itself has momentum that can push physical objects or twist them. This might seem very strange, but it is definitely the case that the electromagnetic field itself can have both. | We have not talked much about linear and angular momentum conservation in an electromagnetic system because they extend beyond the scope of this course. This is because to truly understand the relationship between these and the electromagnetic field, we must develop an understanding that the electromagnetic field can have linear and angular momentum. That's right, the field itself has momentum that can push physical objects or twist them. This might seem very strange, but it is definitely the case that the electromagnetic field itself can have both. |
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| A common example of this comes from astrophysics. When a star is going through fusion, it has a lot of gas pushing outward from the core. In addition, light is carried outward. This is complicated process, but the gas and light run into material in front of them as they move towards the stellar surface. These pushes by the gas and light cause a pressure on the material in front of them; pushing them outward. However, the gas in front of the outward moving gas and light is gravitationally attracted to any matter behind it. This careful balance of the gravitational pressure, gas pressure, and radiation pressure (the momentum imparted by collisions of electromagnetic radiation with material) determines the size, temperature, and brightness of the star. Stellar formation and evolution is vast research topic, but the point is that without that radiation pressure from the momentum carried by the electromagnetic radiation, the star could collapse under it's own gravity -- in fact, this is what happens in core collapse supernovae! | A common example of this comes from astrophysics. When a star is going through fusion, it has a lot of gas pushing outward from the core. In addition, light is carried outward. This is a complicated process, but the gas and light run into the material in front of them as they move towards the stellar surface. These pushes by the gas and light causes pressure on the material in front of them; pushing them outward. However, the gas in front of the outward moving gas and light is gravitationally attracted to any matter behind it. This careful balance of the gravitational pressure, gas pressure, and radiation pressure (the momentum imparted by collisions of electromagnetic radiation with material) determines the size, temperature, and brightness of the star. Stellar formation and evolution is a vast research topic, but the point is that without that radiation pressure from the momentum carried by the electromagnetic radiation, the star could collapse under it's own gravity -- in fact, this is what happens in core-collapse supernovae! |
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| ==== Energy and Charge Conservation in E&M ==== | ==== Energy and Charge Conservation in E&M ==== |
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| === Resistors in a circuit === | === Resistors in a circuit === |
| {{ 184_notes:week8_6.png?300}} | [{{ 184_notes:week8_6.png?300|Resistors in series}}] |
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| [[184_notes:r_series|Two resistors in series]] (end-to-end) must have the same current running through them, but they can use different amounts of electric potential to drive that current depending on their individual resistances. This leads to their combined, effective result on the current in a circuit increasing the resistance of the circuit, | [[184_notes:r_series|Two resistors in series]] (end-to-end) must have the same current running through them, but they can use different amounts of electric potential to drive that current depending on their individual resistances. This leads to their combined, effective result on the current in a circuit increasing the resistance of the circuit, |
| $$R_{eq} = R_1 + R_2$$ | $$R_{eq} = R_1 + R_2$$ |
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| {{184_notes:week8_9.png?400 }} | [{{184_notes:week8_9.png?400|Resistors in parallel }}] |
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| [[184_notes:r_parallel|Two resistors in parallel]] (connected off the same branch) must use the same electric potential (by the loop rule), but they can drive different currents as long as the sum of those currents is equal to the total before the branch splits. This leads to their combine effective result as reducing the overall resistance of the circuit, | [[184_notes:r_parallel|Two resistors in parallel]] (connected off the same branch) must use the same electric potential (by the loop rule), but they can drive different currents as long as the sum of those currents is equal to the total before the branch splits. This leads to their combine effective result as reducing the overall resistance of the circuit, |
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| === Capacitors in a circuit === | === Capacitors in a circuit === |
| {{ 184_notes:week8_12.png?300}} | [{{ 184_notes:week8_12.png?300|capacitors in series}}] |
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| [[184_notes:c_series|Two capacitors in series]] (end-to-end) must have the same amount of stored charge, otherwise a current would be driven until such time that they did. This means that each of them can store a different amount of energy per unit charge, which depends on their individual capacitance. The result is reducing the overall capacitance of the circuit, | [[184_notes:c_series|Two capacitors in series]] (end-to-end) must have the same amount of stored charge, otherwise a current would be driven until such time that they did. This means that each of them can store a different amount of energy per unit charge, which depends on their individual capacitance. The result is reducing the overall capacitance of the circuit, |
| $$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$$ | $$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$$ |
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| {{184_notes:week8_15.png?400 }} | [{{184_notes:week8_15.png?400|Capacitors in parallel }}] |
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| [[184_notes:c_parallel|Two capacitors in parallel]] (connected off the same branch) must use the same energy per unit charge (because of the loop rule), but they can store different amounts of charge depending on their individual capacitances. The result is increasing the overall capacitance of the circuit, | [[184_notes:c_parallel|Two capacitors in parallel]] (connected off the same branch) must use the same energy per unit charge (because of the loop rule), but they can store different amounts of charge depending on their individual capacitances. The result is increasing the overall capacitance of the circuit, |
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| $$C_{eq} = C_1 + C_2$$ | $$C_{eq} = C_1 + C_2$$ |